Geography Reference
In-Depth Information
angular momentum flux is therefore given approximately by
1
1
1
u
(p
s
v)
a cos φdσ
a cos φp
s
u
v
dσ
p
s
Mvdσ
≈
≈
(10.46)
0
0
0
where we have assumed that
th
e fractional change in p
s
is small compared to the
change in v
so that (p
s
v)
≈
p
s
v
. The angular momentum flux is thus proportional
to the negative of the meridional component of the EP flux given in (10.20).
In the Northern Hemisphere, as shown in Fig. 10.6, the eddy momentum flux in
midlatitudes is positive and decreases in magnitude with latitude poleward of 30
◦
.
For quasi-geostrophic flow positive eddy momentum flux requires that the eddies
be asymmetric in the horizontal plane with the trough and ridge axes tilting as
indicated in Fig. 10.11. When the troughs and ridges on the average have southwest
to northeast phase tilt, the zonal flow will be larger than average (u
> 0) where
the meridional flow is pole
ward
(v
> 0) and less than average (u
< 0) where the
flow is equatorward. Thus, u
v
> 0 and the eddies will systematically transport
positive zonal momentum poleward.
As shown in (10.42) the
total
vertical mo
ment
um flux consists of the flux
due to large-scal
e motions p
s
M
σ , the flux due to the pressure
torque, (
a c
os φ) σp
s
∂
∂x , and the flux due to small-scale turbulent stresses,
ga cos φτ
E
. As mentioned previously, the last two are responsible for the transfer
of momentum from the earth to the atmosphere in the tropics and from the atmo-
sphere to the earth in midlatitudes. Outside the planetary boundary layer, however,
the vertical momentum transp
ort i
n the troposphere is due primarily to the vertical
-momentum flux, a cos φp
s
˙
σ
˙
≈
a cos φp
s
˙
σ .
An estimate of the annual average of the zonal-mean total surface torque is
shown in Fig. 10.12. The total surface torque must be balanced by poleward fluxes
of angular momentum in the atmosphere. Except for the belt within 10
◦
of the
equator, almost all of the poleward flux is accounted for by the eddy flux term
given on the right-hand side of (10.46). Thus, the momentum budget and the
energy cycle both depend critically on the transports by the eddies.
Fig. 10.11
Schematic streamlines for a positive eddy momentum flux.
